A046760 Wasteful numbers.
4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 108, 110, 114
Offset: 1
Examples
For n = 125 = 5^3, l(n) = 3 but D(n) = 2. So 125 is not a term of this sequence. [clarified by _Derek Orr_, Jan 30 2015]
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
- J.-P. Delahaye, Les chasseurs de nombres premiers.
- R. G. E. Pinch, Economical numbers., arXiv:math/9802046 [math.NT], 1998.
- Eric Weisstein's World of Mathematics, Wasteful Number.
- Wikipedia, Extravagant number.
Programs
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Haskell
a046760 n = a046760_list !! (n-1) a046760_list = filter (\n -> a050252 n > a055642 n) [1..] -- Reinhard Zumkeller, Aug 02 2013
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Mathematica
Cases[Range[115], n_ /; Length[Flatten[IntegerDigits[FactorInteger[n] /. 1 -> Sequence[]]]] > Length[IntegerDigits[n]]] (* Jean-François Alcover, Mar 21 2011 *)
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PARI
for(n=1,100,s="";F=factor(n);for(i=1,#F[,1],s=concat(s,Str(F[i,1]));s=concat(s,Str(F[i,2])));c=0;for(j=1,#F[,2],if(F[j,2]==1,c++));if(#digits(n)<#s-c,print1(n,", "))) \\ Derek Orr, Jan 30 2015
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Python
from itertools import count, islice from sympy import factorint def A046760_gen(): # generator of terms return (n for n in count(1) if len(str(n)) < sum(len(str(p))+(len(str(e)) if e > 1 else 0) for p, e in factorint(n).items())) A046760_list = list(islice(A046760_gen(),20)) # Chai Wah Wu, Feb 18 2022
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